Solve for $x$ : $3x^2 + 9x - 162 = 0$
Solution: Dividing both sides by $3$ gives: $ x^2 + {3}x {-54} = 0 $ The coefficient on the $x$ term is $3$ and the constant term is $-54$ , so we need to find two numbers that add up to $3$ and multiply to $-54$ The two numbers $9$ and $-6$ satisfy both conditions: $ {9} + {-6} = {3} $ $ {9} \times {-6} = {-54} $ $(x + {9}) (x {-6}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 9) (x -6) = 0$ $x + 9 = 0$ or $x - 6 = 0$ Thus, $x = -9$ and $x = 6$ are the solutions.